Case Study - Group differences based upon deformation maps
Each of the 19 images in this pilot study (9 control images and 10 AD) was stripped of the skull using the automated skullstrip routine described earlier. In most cases the skullstrip produced a relatively clean whole brain which had to be manually further cleaned to remove bits of dura left in patches on the cortex. The manual cleaning phase requires the user to trace and cut off these extraneous bits of tissue from the brain surface. The amount of tracing is considerably less than what would be involved in manually segmenting the brain by tracing it in each slice.
A preliminary template was selected from one of the control subjects, and all other subjects (both controls and AD) were linearly aligned to it. This alignment used 12 parameters, with scaling and shear parameters supplementing the rotations and translations described previously. We used the CC metric to optimize the alignments.
After linear alignment of each subject to the preliminary template, the template was warped to each of these subjects and a vector deformation field computed for each warp. The average deformation vector at each voxel of the template was computed, and then each voxel was deformed by that average deformation. The resulting synthetic image was our Minimal Deformation Template (MDT). It is an image that is “closer” to the mean of all the subjects in the study than our arbitrarily selected preliminary target, thus conducive to better matching with each of the subjects.
After creation of the MDT a second and final set of warps was conducted between the MDT and each of the subjects (including the subject which provided the preliminary target). The final match between each subject and the MDT, evaluated by our CC matching criterion, was indeed better in each case than the matching of each subject and preliminary template.
The warps described here were all done using cubic B-splines. The present warps included a built-in feature that we are currently developing for automatically estimating and correcting for MRI bias field differences between the two images. The goal of this feature is to improve the reliability and robustness of the warps, including the jacobian shape change maps derived from them.
For the cross-sectional matches, we generated images of group differences between the control and AD subjects. These used t-images computed from the averaged and smoothed jacobian maps of each subject warp to the MDT. The t-images highlighted areas where the group difference of the mean jacobians was large compared to the variances at a specific voxel location. We did not use standard Gaussian random field theory to compute t-value significance, since the jacobian fields had been smoothed by tissue type and hence were not continuous. An appropriate analysis of significance would therefore involve a non-parametric approach.
Figure A template is warped against 9 controls and 10 AD patients. The jacobians of these warps are averaged for each population. Then the two averages are subtracted and normalized to produce a t-value at each voxel. To visualize, voxels with extreme t-values are assigned bright colors to display regions of significant difference.
The following figure includes a t-image derived from the difference of the mean jacobian images, AD group minus control group. Higher values, represented in lighter tones, indicate greater expansion of the template on average to match the AD subjects in a given location, and hence an expansion of the local space relative to the controls; darker tones indicate a greater contraction relative to the controls.
Figure Left: Average jacobian of the warps for the controls. Middle: Same for AD patients. Right: Difference of these, with threshholded t-values displayed in orange colors.
The t-values in this image are not extreme (in the hippocampal regions they are in the range of -4.0) but they do indicate areas of anatomical difference between the two groups. Because the jacobian fields are evidently not continuous (see the discrete boundaries in the left image) the significance of the t-values cannot be assessed using spm-style techniques of Gaussian random fields.